A new balance index for phylogenetic trees

@article{Mir2013ANB,
  title={A new balance index for phylogenetic trees},
  author={Arnau Mir and Francesc Rossell{\'o} and Luc{\'i}a Rotger},
  journal={Mathematical biosciences},
  year={2013},
  volume={241 1},
  pages={
          125-36
        }
}
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60 Citations
Highly Influential Citations
10
Background Citations
32
Methods Citations
16
Results Citations
1

60 Citations

Extremal properties of the Colless balance index for rooted binary trees
TLDR
The analysis of the minimal value of the Colless index and the characterization of trees that achieve it, are much more involved than usual and are focused on its extremal properties.
A balance index for phylogenetic trees based on quartets
We define a new balance index for phylogenetic trees based on the symmetry of the evolutive history of every quartet of leaves. This index makes sense for polytomic trees and it can be computed in…
Squaring within the Colless index yields a better balance index
Sound Colless-like balance indices for multifurcating trees
TLDR
A family of Colless-like balance indices CD,f are proposed that generalize the Colless index to multifurcating phylogenetic trees and the results show that the growth pace of the function f influences the notion of “balance” measured by the indices it defines.
On the minimum value of the Colless index and the bifurcating trees that achieve it
TLDR
This manuscript derives both recursive and closed expressions for the minimum Colless index of a tree with n leaves and shows a connection between these expressions and the so-called Blancmange curve, a fractal curve, which is another popular balance index.
Extremal values of the Sackin balance index for rooted binary trees
TLDR
This manuscript fully characterize trees with minimal and maximal Sackin index and also provides formulas to explicitly calculate the number of such trees.
A simple derivation of the mean of the Sackin index of tree balance under the uniform model on rooted binary labeled trees.
Extremal Values of the Sackin Tree Balance Index
TLDR
This manuscript extends the findings on trees with minimal and maximal Sackin indices from the literature on ordered trees and subsequently uses the results to provide formulas to explicitly calculate the numbers of such trees, as well as analyzing the case when the underlying trees need not be binary.
Robust, Universal Tree Balance Indices
TLDR
A new class of robust, universal tree balance indices are defined that take a form similar to Colless’ index but account for node sizes, are defined for trees with any degree distribution, and enable more meaningful comparison of trees with different numbers of leaves.
A new resolution function to evaluate tree shape statistics
TLDR
A new resolution function to evaluate the power of different tree shape statistics to distinguish between dissimilar trees is proposed and it is shown that the newresolution function requires less time and space in comparison with the previously proposed resolution function.
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References

SHOWING 1-10 OF 38 REFERENCES
CENTRAL MOMENTS AND PROBABILITY DISTRIBUTION OF COLLESS'S COEFFICIENT OF TREE IMBALANCE
  • J. S. Rogers
  • Biology
    Evolution; international journal of organic evolution
  • 1994
TLDR
Recursion equations are developed that allow exact calculation of the mean, variance, skewness, and complete probability distribution of I for two different probability‐generating models for bifurcating tree shapes and illustrate how these theoretically derived probabilities and parameters may be used to test whether the evolution of a monophyletic group or set of monophyletsic groups has proceeded according to a Markov model with equal rates of speciation and extinction.
Properties of phylogenetic trees generated by Yule-type speciation models.
On statistical tests of phylogenetic tree imbalance: the Sackin and other indices revisited.
CENTRAL MOMENTS AND PROBABILITY DISTRIBUTIONS OF THREE MEASURES OF PHYLOGENETIC TREE IMBALANCE
Several recent studies have included attempts to use the balance of phylogenetic trees, i.e., the extent to which sister groups within a tree tend to be the same size, to test hypotheses about the…
Which random processes describe the tree of life? A large-scale study of phylogenetic tree imbalance.
TLDR
The most popular model of phylogenetic trees is a branching process introduced by Yule, in which lineages split at random (Yule, 1924), and here the study of one major database of published phylogenies is reported.
Probability distributions of ancestries and genealogical distances on stochastically generated rooted binary trees.
  • W. Mulder
  • Mathematics
    Journal of theoretical biology
  • 2011
The mean value of the squared path-difference distance for rooted phylogenetic trees
Exact formulas for the variance of several balance indices under the Yule model
One of the main applications of balance indices is in tests of null models of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number…
PHYLOGENETIC ANALYSIS: MODELS AND ESTIMATION PROCEDURES
TLDR
This paper shows how suitable evolutionary models can be constructed and applied objectively and how the type of data will affect both the method of treatment and the validity of the results.
Optimization Over a Class of Tree Shape Statistics
TLDR
This chapter concludes with a successful application of the methods to find a new statistic which indicates a significant difference between two distributions on trees which were previously postulated to have similar properties.
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